FISHERY BULLETIN: VOL. 81, NO. 2 



n = 10 



25,000 



20 



40 



60 



80 100 120 140 



Number of Species (n) 



160 



180 



FIGURE 2. — Relationship between I and the number of species (n) 

 for associations with different abundances (x,-) and heterogeneity {q). 

 In all cases, diversity (//') = 1.0. For each curve, total number of in- 

 dividuals (T) is a constant. Curves are derived from Appendix Equa- 

 tion (7). 



and the underlying community structure is opposite 

 in direction from that oil. However, the behavior of 

 a 2 (I) is mediated somewhat by the simultaneous 

 dependence of the factor /? on community structure 

 (Figs. 4,5). Thus, although I shows a negative re- 

 lationship with numbers of species, the relationship 

 between <7 2 (7 ) and n is also inverse, but much weaker 

 (Kendall correlation, 0.05 < P < 0.10). While I de- 

 creases continuously with increasing diversity, o 2 (I) 

 increases with diversity, but stabilizes or decreases 

 at high diversities. The dominant influence on the 

 variance of/ is the population heterogeneity, q. As 



0.3 0.4 0.5 0.6 0.7 

 DIVERSITY (H') 



0.8 



FIGURE 3. — Relationship between / and diversity (If) for associa- 

 tions with different numbers of species (n), total abundance (T), and 

 heterogeneity (<j). Curves are derived from Appendix Equation (7). 

 X's indicate values of/ observed in computer simulation and are in- 

 cluded to indicate the accuracy of the equation. 



evident from Appendix Equation (9), an order-of- 

 magnitude increase in q produces an order-of- 

 magnitude increase in a 2 {I ). 



CONSIDERATION OF 

 ASSUMPTIONS 



Two assumptions underlying this study are admit- 

 tedly unrealistic and require further consideration: 



0.4 

 035 

 0.3 

 QQ. 0.25 

 0.2 

 0.15 

 0.1 

 05 



_L 



_L 



20 



_L 



J. 



40 



_L 



60 



J_ 



_L 



140 



160 



_L 



180 



X 



J 



200 



80 100 120 



Number of Species ( n ) 

 FIGURE 4. — Relationship between the value of /3 in Appendix Equation (9) and the number of species (n). Vertical bars are 95?; confidence 

 intervals from five estimates with diversity (W) = 1.0 and heterogeneity (q) = 0.1, 0.5, 1.0, 5.0, and 10. Dots are single estimates. Open cir- 

 cles are maximum values of ft observed when H' varied from 0.0 to 1.0. Shaded area approximately delimits the range of observed 

 values of /?. 



378 



